Test Review - Answers


Test Review - Answers
Pre-Calculus: Chapter 4 Review
Name: ______________________
This are problems that supplement the textbook review: pg.439: 1,5,13,19, 23, 29, 33, 35, 37, 41, 5155, 63. 75, 79,
81, -- 71, 85, 87, 97, 102
1. Find the exact values of the six trig functions of the angle Ѳ shown to
the right.
2. Find the five remaining trig functions of Ѳ, given
that sec  , tan   1
3. On graph paper, graph the function for two full cycles:
y  2 cos( x)  3
1  x
y   sin  
2 4
4. Find an equation for the
following graph.
5. Kylie measures the
angle of elevation from
a point on level ground
to the top of a building 120 meters high to be 32o . She walks towards the building until the angle of
elevation is 45o . How far does she walk?
6. Find all values of theta between 0    2 that satisfies the following equation. Do not use your
calculator for part a.
a. cot    3
b. sec  1.743
7. The following graph shows the depth of water, y
metres, at a point P, during one day.
The time t is given in hours, from midnight to noon.
Use the graph to write down an estimate of
the value of t when
the depth of water is minimum;
the depth of water is maximum;
The depth of water can be modelled by the
function y = A cos (B (t – 1)) + C.
Show that A = 8.
Write down the value of C.
Find the value of B.
A sailor knows that he cannot sail past P when the depth of the water is less than 12 m. Calculate the
values of t between which he cannot sail past P.
8. A Ferris wheel with centre O and a radius of 15 metres is represented in the diagram below. Initially seat A is at
ˆB = π .
ground level. The next seat is B, where AO
Find the length of the arc AB.
Find the area of the sector AOB.
The wheel turns clockwise through an angle of
. Find the height of A above the ground.
The height, h metres, of seat C above the ground after t minutes, can be modelled by the function
h (t) = 15 − 15 cos  2t   .
Find the height of seat C when t =
Find the initial height of seat C.
Find the time at which seat C first reaches its highest point.